Factor x^3-2x^2-x+2

Problem

x3−2*x2−x+2

Solution

1. Group the terms into two pairs to prepare for factoring by grouping.

(x3−2*x2)+(−x+2)

2. Factor out the greatest common factor from each group.

x2*(x−2)−1*(x−2)

3. Factor out the common binomial (x−2) from the expression.

(x2−1)*(x−2)

4. Identify the difference of squares in the first factor, x2−1 which follows the pattern a2−b2=(a−b)*(a+b)

(x−1)*(x+1)*(x−2)

Final Answer

x3−2*x2−x+2=(x−1)*(x+1)*(x−2)

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